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Full text of "Solar project description for Reedy Creek Utilities, Co., Inc. office building"

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SOLAR/2014-79/14 




Solar Energy System 
Performance Evaluation 



BLAKEDALE PROFESSIONAL CENTER 

OFFICE UNIT 

Greenwood, South Carolina 

October, 1978 through March, 1979 



U.S. Department of Energy 

National Solar Heating and 
Cooling Demonstration Program 

National Solar Data Program 




NOTICE 

This report was prepared as an account of work sponsored by the United States 
Government. Neither the United States nor the United States Department of Energy, nor 
any of their employees, nor any of their contractors, subcontractors, or their employees, 
makes any warranty, express or implied, or assumes any legal liability or responsibility for 
the accuracy, completeness or usefulness of any information, apparatus, product or process 
disclosed, or represents that its use would not infringe privately owned rights. 



This report has been reproduced directly from the best available copy. 



Available from the National Technical Information Service, U. S. Department of 
Commerce, Springfield, Virginia 22161. 



Price: Paper Copy $5.25 
Microfiche $3.00 



SOLAR/2014-79/14 

Distribution Category UC-59 



SOLAR ENERGY SYSTEM PERFORMANCE EVALUATION 



BLAKEDALE PROFESSIONAL CENTER 

OFFICE SUITE 

GREENWOOD, SOUTH CAROLINA 



OCTOBER 1978 THROUGH MARCH 1979 



JOSEPH A. THOMAS, PRINCIPAL AUTHOR 

WILLIAM H. McCUMBER, MANAGER OF PERFORMANCE ANALYSIS 

LARRY J. MURPHY, IBM PROGRAM MANAGER 



IBM CORPORATION 
150 SPARKMAN DRIVE 
HUNTSVILLE, ALABAMA 35805 



PREPARED FOR THE 
DEPARTMENT OF ENERGY 
OFFICE OF ASSISTANT 
SECRETARY FOR 
CONSERVATION AND SOLAR APPLICATIONS 
UNDER CONTRACT EG-77-C-01-4049 
H. JACKSON HALE, PROGRAM MANAGER 



TABLE OF CONTENTS 

SECTION TITLE PAGE 

1. FOREWORD 1 

2. SUMMARY AND CONCLUSIONS 3 

.3. SYSTEM DESCRIPTION 7 

4. PERFORMANCE EVALUATION TECHNIQUES 11 

5. PERFORMANCE ASSESSMENT 13 

5.1 Weather Conditions 14 

5.2 System Thermal Performance 16 

5.3 Subsystem Performance 19 

5.3.1 Collector Array Subsystem 20 

5.3.2 Storage Subsystem 28 

5.3.3' Hot Water Subsystem 32 

5.3.4 Space Heating Subsystem 33 

5.4 Operating Energy 36 

5.5 Energy Savings 38 

6. REFERENCES 41 

APPENDIX A DEFINITION OF PERFORMANCE FACTORS AND SOLAR TERMS. . . A-l 
APPENDIX B SOLAR ENERGY SYSTEM PERFORMANCE EQUATIONS FOR THE 

BLAKEDALE PROFESSIONAL CENTER B-l 

APPENDIX C LONG-TERM AVERAGE WEATHER CONDITIONS C-l 



n 



LIST OF FIGURES AND TABLES 



FIGURE 



TITLE 



PAGE 



3-1 



Blakedale Professional Center Solar Energy 
System Schematic 



5.3.1-1 



Collector Array Operating Point 
Histogram and Instantaneous 
Efficiency Curves .... 



26 



TABLE 



TITLE 



PAGE 



5.1-1- 

5.2-1 

5.2-2 

5.3.1-1 

5.3.1-2 

5.3.2-1 

5.3.4-1 

5.4-1 

5.5-1 



Weather Conditions 15 

System Thermal Performance 17 

Solar Energy System Coefficients 

of Performance 18 

Collector Arjsay Performance 21 

Energy Gain Comparison 24 

Storage Subsystem Performance 30 

Heating Subsystem Performance 34 

Operating Energy 37 

Energy Savings 39 



m 



NATIONAL SOLAR DATA PROGRAM REPORTS 

Reports prepared for the National Solar Data Program are numbered under a 
specific format. For example, this report for the Blakedale Professional 
Center project site 1s designated as SOLAR/2014-79/14. The elements of 
this designation are explained 1n the following illustration: 



Prepared for the 

National Solar 

Data Program 



Demonstration Site 



SOLAR /2014-79/14 



Report Type 
Designation 



Year 



• Demonstration Site Number: 

Each Project site has its own discrete number - 1000 through 1999 
for residential sites and 2000 through 2999 for commercial sites. 

t Report Type Designation: 

This number identifies the type of report, e.g., 

Monthly Performance Reports are designated by the numbers 01 
(for January) through 12 (for December). 

Solar Energy System Performance Evaluations are designated 
by the number 14. 

Solar Project Descriptions are designated by the number 50. 

Solar Project Cost Reports are designated by the number 60. 

These reports are disseminated through the U. S. Department of Energy, 
Technical Information Center, P. 0. Box 62, Oak Ridge, Tennessee 37830. 



IV 



1 . FOREWORD 

The National Program for Solar Heating and Cooling is being conducted by 
the Department of Energy under the Solar Heating and Cooling Demonstration 
Act of 1974. The overall goal of this activity is to accelerate the 
establishment of a viable solar energy industry and to stimulate its growth 
in order to achieve a substantial reduction in non-renewable energy resource 
consumption through widespread applications of solar heating and cooling 
technology. 

Information gathered through the Demonstration Program is disseminated in a 
series of site-specific reports. These reports are issued as appropriate, 
and may include such topics as: 

Solar Project Description 

Design/Construction Report 

Project Costs 

Maintenance and Reliability 

Operational Experience 

Monthly Performance 

System Performance Evaluation 

The International Business Machines Corporation is contributing to the over- 
all goal of the Demonstration Act by monitoring, analyzing, and reporting the 
thermal performance of solar energy systems through analysis of measurements 
obtained by the National Solar Data Program. 

The System Performance Evaluation Report is a product of the National Solar 
Data Program. Reports are issued periodically to document the results of 
analysis of specific solar energy system operational performance. This 
report includes system description, operational characteristics and capa- 
bilities, and an evaluation of actual versus expected performance. The 
Monthly Performance Report, which is the basis for the System Performance 
Evaluation Report, is published on a regular basis. Each parameter 



presented 1n these reports as characteristic of system performance repre- 
sents over 8,000 discrete measurements obtained each month by the National 
Solar Data Network. 

All reports issued by the National Solar Data Program for the Blakedale 
Professional Center solar energy system are listed in Section 6, References. 

This Solar Energy System Performance Evaluation Report presents the results 
of a thermal performance analysis of the Blakedale Professional Center solar 
energy system. The analysis covers operation of the system from October 1978 
through March 1979. A detailed system description is contained in Section 3. 
Analysis of the system thermal performance was accomplished using a system 
energy balance technique described in Section 4. Section 2 presents a sum- 
mary of the results and conclusions obtained while Section 5 presents a de- 
tailed assessment of the system thermal performance. 

Acknowledgements are extended to those individuals involved in the operation 
of the Blakedale Professional Center solar energy system. Their insight and 
cooperation in the resolution of various on-site problems during the report- 
ing period were invaluable. 



2. SUMMARY AND CONCLUSIONS 

This System Performance Evaluation Report provides an operational summary 
of the solar energy system installed at the Blakedale Professional Center 
Office Suite in Greenwood, South Carolina. This analysis is conducted by 
evaluation of measured system performance and by comparison of measured 
weather data with long-term average climatic conditions. The performance 
of major subsystems is also presented. 

The measurement data were collected (References [7 - 12])* by the National 
Solar Data Network(NSDN) [1] for the period October 1978 through March 
1979. System performance data are provided through the NSDN via an IBM- 
developed Central Data Processing System (CDPS) [2], The CDPS supports 
the collection and analysis of solar data acquired from instrumented sys- 
tems located throughout the country. This data is processed daily and 
summarized into monthly performance reports. These monthly reports form 
a common basis for system evaluation and are the source of the performance 
data used in this report. 

Features of this report include: a system description, a review of actual 
system performance during the report period, analysis of performance based 
on evaluation of meteorological load and operational conditions, and an 
overall discussion of results. 

Monthly values of average daily insolation and average outdoor ambient tem- 
perature measured at the Blakedale Professional Center site are presented 
in Table 5.1-1. Also presented in the table are the long-term, average 
monthly values for these climatic parameters. 

The energy collection and storage subsystem commenced operation on October 
16, 1978 for the current heating season. By mid December, collector 



*Numbers in brackets designate References found in Section 6. 



circulating pump PI frequently failed to start automatically when solar 
energy was available at the collectors, although it always stopped auto- 
matically. For this reason, the resident contractor monitored the opera- 
tion of this pump and manually started it after the control system had 
failed. This semi-automatic operation continued until April 19, 1979, at 
which time the heating season terminated. This control system failure 
resulted in less than optimal energy collection through the heating season. 

Even when pump PI started automatically, it was frequently premature, 
resulting in unintentional energy rejection by the collector array. The 
pump also continued to run after there was no energy gain by the collec- 
tors. As a result, solar energy was transferred from thermal storage to 
the collectors and subsequently dissipated to the environment for short 
periods of time. This loss was accelerated whenever the pump cycled 
frequently, as during periods of low level and intermittent insolation. 

The collector array subsystem was not operational from March 25 through 
March 29, 1979. Cumulative evaporation losses from the open storage system 
reduced the amount of water in thermal storage to a level that prevented 
pump PI from circulating the water to the collectors. 

The domestic hot water subsystem was operational over the entire six month 
period except for one week. On February 20, 1979, a leak developed in the 
pipe between heat exchanger HX1 and flow rate sensor W300. As a result, 
approximately 0.73 million Btu of solar energy were lost to the environment 
before this leak was discovered and subsequently repaired. 

The space heating subsystem commenced operation on October 18, 1978 for 
the current heating season. However, the subsystem was not operational 
from December 27, 1978 through January 1, 1979 and from March 25 through 
March 29, 1979. In both cases, cumulative evaporation losses from the 
system reduced the amount of water in thermal storage to a level that 
prevented pump P2 from circulating the water that delivers solar energy 
to heat exchanger HX2. 



Prior to mid January, pump P2 started whenever there was a demand for heat- 
ing, even when there was no available solar energy in thermal storage. For 
this reason, the resident contractor modified the control system whereby he 
manually operated this pump as appropriate. By March, this procedure was 
modified so that the pump ran continuously. This semi-automatic operation 
permitted the control system to transfer solar energy from storage to either 
heat exchanger HX2 or around this heat exchanger as governed by the position 
of the motorized valve. This mode of operation resulted in an increased 
operating energy expenditure and increased energy transport losses. 

During the six month period from October 1978 through March 1979, 14 percent 
(12.39 million Btu) of the 86.54 million Btu system load was provided by solar 
energy, resulting in a net electrical energy savings of 4.69 million Btu. 

During the reporting period, the measured average outside ambient temperature 
was 53°F, or two degrees higher than the long-term average of 51 °F. As a 
result, a total of 2,296 heating degree-days were accumulated as opposed to 
the long-term expected total of 2,727. The measured average daily insolation 
in the plane of the collector array was 1,267 Btu/ft^, which was seven per- 
cent below the long r term daily average of 1,357 Btu/ft^. Both long-term 
values are computed from averages derived from the weather station in Green- 
ville, South Carolina. 

A total of 220.45 million Btu of solar energy were incident upon the collector 
array during the reporting period. When the collector array was operating, a 
total of 124.27 million Btu was incident on the array. The subsystem collec- 
ted 33.29 million Btu, which represents an operational collector efficiency 
of 27 percent. 

A total of 30.69 million Btu of solar energy was delivered to storage, and 
14.31 million Btu were removed from storage. From this, 12.39 million Btu 
were delivered to the space heating load. The difference represents trans- 
port losses. The average effective storage heat loss coefficient was 102 
Btu/Hr-°F. The variations among the individual monthly values used to 



compute the effective storage heat transfer coefficient, and hence, the vari- 
ations in the coefficient itself are attributable to the unusual operating 
circumstances. 

There was essentially no requirement for water from the domestic hot water 
subsystem during the reporting period. Therefore, no performance data for 
this subsystem has been included in this report. 

The space heating load was 86.54 million Btu for the reporting period. Solar 
energy provided 12.39 million Btu of this total, and the remaining 74.15 mil- 
lion Btu were supplied by the heat pump and electrical resistance heater. 
This resulted in a heating solar fraction of 14 percent, and a net savings of 
4.69 million Btu of electrical energy. 

In general, the Blakedale Professional Center solar energy system performance 
was not up to expectations during this six-month period. System problems of 
significance were the intermittent operation of both the energy collection 
and storage subsystem and the space heating subsystem, and modifications to 
the associated control system, which resulted in excessive and inefficient 
operation of the collection and solar space heating subsystems. 



3. SYSTEM DESCRIPTION 

The Blakedale Professional Center solar energy system is designed to provide 
85 percent of the space heating requirements and 100 percent of the domestic 
hot water heating requirements for a 4,400 square foot office suite in Green- 
wood, South Carolina. Solar energy is collected by 53 flat-plate collectors, 
which are manufactured by PPG Industries. The collectors, having a gross 
area of 954 square feet, are mounted on the roof in three banks. Each col- 
lector array faces south at an angle of 45 degrees from the horizontal. The 
heat transfer medium is 99 percent water and one percent corrosion inhibitor. 
Solar energy is stored in a 5,000-gallon tank buried under the parking lot. 
The tank is insulated with four inches of sprayed-on polyurethane covered with 
a waterproof coating. When solar energy is inadequate, auxiliary space heat- 
ing is provided by a 10-ton heat pump and a 36-kilowatt electric resistance 
heater. Auxiliary hot water is provided by a 40-gallon electric heater. 
Freeze protection is provided by a drain-down system. 

The system, shown schematically in Figure 3-1, has four modes of operation: 

Mode 1 - Collector-to-Storage : This mode is entered when the difference 
between the temperature of the collector and the temperature of water near 
the bottom of the water thermal storage is greater than 19°F. Pump PI cir- 
culates water through the collectors to transfer solar energy to the water 
thermal storage. This mode terminates when the temperature differential 
is less than 6°F, or the temperature of water in the collector is less than 
37°F. 

Mode 2 - Storage-to-Office Area (Solar) : This mode is entered when heat is 
required in the office area. Pump P2 circulates water through the water 
thermal storage to heat exchanger HX2 in the air-handling unit. This mode 
terminates when the supply air temperature is greater than 120°F, or the 
requirement for heat is satisfied. 



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Mode 3 - Sto rage- to-Off ice Area (Auxiliary) : Although this mode is not a 
solar mode of operation, it is entered concurrently with Mode 2 when heat 
is required in the office and the office return air temperature is less 
than 65°F. A 10-ton heat pump is energized to provide heat to heat ex- 
changer HX3. When the outside air temperature is less than 40°F, two 18- 
kilowatt electric resistance heaters are energized in stages to provide aux- 
iliary energy to heat exchanger HX4. This mode terminates when the office 
return air temperature is greater than 68°F, or the requirement for heat is 
satisfied. 

Mode 4 - Domestic Hot Water Heating : This mode is entered when there is a 
requirement for hot water. As hot water is drawn, cold water passes through 
heat exchanger HX1 in the water thermal storage, and subsequently through 
the water heater and tempering valve to provide 120°F. This mode terminates 
when the requirement for hot water is satisfied. 



4. PERFORMANCE EVALUATION TECHNIQUES 

The performance of the Blakedale Professional Center solar energy system 1s 
evaluated by calculating a set of primary performance factors which are 
based on those proposed in the intergovernmental agency report "Thermal Data 
Requirements and Performance Evaluation Procedures for the National Solar 
Heating and Cooling Demonstration Program" [3]. These performance factors 
quantify the thermal performance of the system by measuring the amount of 
energies that are being transferred between the components of the system. 
The performance of the system can then be evaluated based on the efficiency 
of the system 1n transferring these energies. 

Data from monitoring instrumentation located at key points within the solar 
energy system are collected by the National Solar Data Network. This data 
is first formed into factors showing the hourly performance of each system 
component, either by summation or averaging techniques, as appropriate. 
The hourly factors then serve as a basis for the calculation of the daily 
and monthly performance of each component subsystem. 

Each month a summary of overall performance of the Blakedale Professional 
Center site and a detailed subsystem analysis are published. Monthly reports 
for the period covered by this System Performance Evaluation, October 1978 
through March 1979, are available from the Technical Information Center, 
Oak Ridge, Tennessee 37830. 



11 



5. PERFORMANCE -ASSESSMENT 

The performance of the Blakedale Professional Center solar energy system has 
been evaluated for the October 1978 through March 1979 time period. Two per- 
spectives have been taken in this assessment. The first looks at the overall 
system view in which the total solar energy collected, the system load and the 
measured values for solar energy used and system solar fraction are presented. 
Also presented, where applicable, are the expected values for solar energy 
used and system solar fraction. The expected values have been derived from a 
modified f-chart* analysis which uses measured weather and subsystem loads as 
inputs. The model used in the analysis is based on manufacturers' data and 
other known system parameters. In addition, the solar energy system coeffi- 
cient of performance (COP) at both the system and subsystem level has been 
presented. The second view presents a more in-depth look at the details re- 
lating to the performance of individual components. Details relating to the 
performance of the collector array and storage subsystems are presented first, 
followed by details pertaining to the domestic hot water subsystem and the 
space heating subsystem. Included in this area are all parameters pertinent 
to the operation of each individual subsystem. 

The performance assessment of any solar energy system is highly dependent on 
the prevailing weather conditions at the site during the period of perform- 
ance. The original design of the system is generally based on the long-term 
averages for available insolation and temperature. Deviations from these 
long-term averages can significantly affect the performance of the system. 
Therefore, before beginning the discussion of actual system performance, a 
presentation of the measured and long-term averages for critical weather para- 
meters has been provided. 



* f-chart is the designation of a procedure for designing solar heating 
systems. It was developed by the Solar Energy Laboratory, University 
of Wisconsin-Madison. 



13 



5.1 Weather Conditions 

Monthly values of the total solar energy incident in the plane of the collec- 
tor array and the average outdoor temperature measured at the Blakedale Pro- 
fessional Center site during the report period are presented in Table 5.1-1. 

Also presented in Table 5.1-1 are the corresponding long-term average 
monthly values of the measured weather parameters. These data are taken 
from Reference Monthly Environmental Data for Systems in the National Solar 
Data Network [4]. A complete yearly listing of these values for the site 
is given in Appendix C. 

Monthly values of heating and cooling degree-days are derived from daily 
values of ambient temperature. They are useful indications of the system 
heating and cooling loads. Heating degree-days and cooling degree-days are 
computed as the difference between daily average temperature and 65°F. For 
example, if a day's average temperature was 60°F, then five heating degree- 
days are asccumulated. Likewise, if a day's average temperature was 80°F, 
then 15 cooling degree-days are summed monthly. 

During the period from October 1978 through March 1979, the temperature in 

Greenwood, South Carolina was higher than normal as evidenced by a measured 

average outside ambient temperature of 53°F when compared to the long-term 

value of 51 °F. In addition, the cloud cover was greater than normal, as 

evidenced by the measured average daily insolation in the plane of the col- 

lector array of 1,267 Btu/ft , as compared to the long-term daily average 

2 
value of 1,357 Btu/ft . As a result, the requirement for space heating was 

smaller than normal, as was the amount of solar energy available for collec- 
tion over this six-month period. Both long-term values are computed from 
averages derived from the weather station at Greenville, South Carolina. 



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5.2 System Thermal Performance 

The thermal performance of a solar energy system is a function of the total 
solar energy collected and applied to the system load. The total system load 
is the sum of the energy requirements, both solar and auxiliary thermal, for 
each subsystem. The portion of the total load provided by solar energy is 
defined to be the solar fraction of the load. This solar fraction is the 
measure of performance for the solar energy system when compared to design or 
expected solar contribution. 

The thermal performance of the Blakedale Professional Center solar energy sys- 
tem is presented in Table 5.2-1 and Table 5.2-2. This performance assessment 
is based on the six-month period from October 1978 through March 1979. 

During the period from October 1978 through March 1979, 14 percent (12.39 mil- 
lion Btu) of the 86.54 million Btu system load was provided by solar energy, 
compared to the expected system solar fraction of 67 percent (57.90 million 
Btu). These differences were due primarily to the control system problems 
and other system abnormalities that occurred during the reporting period. 

The solar energy system COP (defined as the total solar energy delivered to 
the load divided by the total solar energy system operating energy) was 3.68 
for the six-month period. The collector array subsystem COP and the space 
heating subsystem solar COP for the six-month period were 23.78 and 6.29, 
respectively. These values again relate the amount of solar energy asso- 
ciated with a particular subsystem to the amount of electrical energy re- 
quired to operate the solar portion of that subsystem. As such, the COP 
serves as an indicator of both how well the system was designed and how 
well it operated. At the Blakedale Professional Center site the solar 
energy supplied to the total load is the same as the solar energy supplied 
to the space heating load, and this is the reason that the overall system 
COP appears low with respect to the space heating COP. 



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18 



5.3 Subsystem Performance 

The Blakedale Professional Center solar energy Installation may be 
divided Into four subsystems: 

1 ) Collector array 

2) Storage 

3) Domestic hot water 

4) Space heating. 

Each subsystem is evaluated by the techniques defined 1n Section 4 and 1s 
numerically analyzed each month for the monthly performance reports. This 
section presents the results of integrating the monthly data available on 
the four subsystems for the period October 1978 through March 1979. 



19 



5.3.1 Collector Array Subsystem 

Collector array performance 1s described by comparison of the collected 
solar energy to the incident solar energy. The ratio of these two energies 
represents the collector array efficiency which may be expressed as 



n, 



-0,/Q, 0) 



where: n = Collector Array Efficiency (CAREF) 



c 



Q c = Collected Solar Energy (SECA) 



<s 



Qj = Incident Solar Energy (SEA). 

The gross collector array area is 954 square feet. The measured monthly 
values of incident solar energy, collected solar energy, and collector 
array efficiency are presented in Table 5.3.1-1. 

Evaluation of collector efficiency using operational incident energy and 
compensating for the difference between gross collector array area and 
the gross collector area yields operational collector efficiency. Opera- 
tional collector efficiency, n . is computed as follows: 



n 



CO ^s' 




Qc/ Q„-x^ (2) 



where: Q = Collected Solar Energy (SECA) 

Q j = Operational Incident Energy (SEOP) 

A = Gross Collector Area (product of the number 
p of collectors and the total envelope area of 
one unit) (GCA) 

A a = Gross Collector Array Area (total area perpen- 



a 



dicular to the solar flux vector including all 
mounting, connecting and transport hardware (GCAA). 



Note: The ratio -#^1s typically 1.0 for most collector array configurations 



20 



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21 



This latter efficiency term is not the same as collector efficiency as rep- 
resented by the ASHRAE Standard 93-77 [5]. Both operational collector ef- 
ficiency and the ASHRAE collector efficiency are defined as the ratio of 
actual useful energy collected to solar energy incident upon the collector 
and both use the same definition of collector area. However, the ASHRAE 
efficiency is determined from instantaneous evaluation under tightly con- 
trolled, steady state test conditions, while the operational collector ef- 
ficiency is determined from the actual conditions of daily solar energy 
system operation. Measured monthly values of operational incident energy 
and computed values of operational collector efficiency are also presented 
in Table 5.3.1-1. 

Collector Array efficiency may be viewed from two perspectives. The first 
assumes that the efficiency be based upon all available solar energy; how- 
ever, that point of view makes the operation of the control system a part 
of array efficiency. For example, energy may be available at the collector, 
but the collector fluid temperature is below the control minimum, thus the 
energy is not collected. The monthly efficiency computed by this method is 
listed in the column entitled "Collector Array Efficiency" in Table 5.3.1-1. 

The second viewpoint assumes the efficiency be based upon only the incident 
energy during periods of collection. The monthly efficiency computed by 
this method is listed in the column entitled "Operational Collector Array 
Efficiency." Efficiency computed by this method is used in the following 
discussion. 

The Blakedale Professional Center collector array consists of 53 flat-plate 
collectors that are arranged into three banks on the roof. The lowest bank 
contains 23 panels whereas each of the other banks contains 15 panels. Each 
bank faces south at an angle of 45 degrees from the horizontal. The heat 
transfer medium is 99 percent water and one percent of corrosion inhibitor. 
The Collector-to-Storage Mode (Mode 1) is entered when the temperature of 
the collector is 19°F greater than the temperature of water in thermal stor- 
age. This mode is terminated when the temperature difference is less than 
6°F, or the temperature of the collector is less than 37°F. 



22 



The energy collection and storage subsystem was operational from October 16, 
1978 through March 24, 1979 and after March 29, 1979. Due to a control mal- 
function pump PI did not always start automatically after mid December. The 
operational efficiency ranged from 22 percent in November to 32 percent in 
March, and averaged 27 percent. A total of 33.29 million Btu was collected 
out of a total of 124.27 million Btu that were incident on the collector ar- 
ray when 1t was operating. Table 5.3.1-2 presents a comparison of the actual 
performance of the collector array for the month of March. March was chosen 
as the example month because the measured insolation was approximately equal 
to the long-term average and the collector array was operational during most 
of the month. 

Instantaneous efficiency curves are derived from laboratory test data sup- 
plied by the collector manufacturer and from empirical sources. The three 
empirically derived curves are: a linear regression line fit through field 
data obtained in March; a linear regression line fit through all field data 
in the base; and a curvilinear (second order) regression line fit through 
all field data in the base (the base data consists of all measurments relat- 
ing to collector array performance made from October 1978 through March 1979). 

Each error value presented 1n the error field of Table 5.3.1-2 1s computed 
by the equation 

error = (A - P) / P (3) 

where: 

A 1s the actual energy gain of the collector array shown 1n 
column one (million Btu/day) 

P 1s the predicted energy gain of the collector array based on 
projecting the measured operating point to the applicable in- 
stantaneous efficiency curve and multiplying by the measured 
insolation level and collector array area and then summing 
over all the measured operating points (million Btu/day). 



23 





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24 



The computed error is then a measure of how well the particular prediction 
curve fits tre reality of dynamic operating conditions in the field. The 
data presented in Table 5.3.3-2 indicates a strong disparity between per- 
formance predictions based on single panel laboratory tests and actual re- 
sults obtained from field operation of this array of panels. 

The slight difference shown for solar energy collected during March in 
Table 5.3.1-1 and Table 5.3.1-2 ts primarily due to the abnormal operation 
cf :u"c PI 2 n : the 'act t r a: r c rejectee e r e T *g.. ■' s included in the compu- 
tations usee tfl generate tne cata :res£"te: •> Table 5.3.1-2. 

Figure 5.3.1-1 presents a histogram of the collector arra> crerating points 
for March. Also presented in Figure 5.3.1-1 are linear instantaneous effi- 
ciency curves Dased on controlled labcratory test data supplied by the col- 
lector manufacturer, field aata for the month of March and long-tenn field 
data for the base period. The ordinate of the graph shown in Figure 5.3.1-1 
has a printed range of to 10 percent to display the distribution of 
collector array operating points. However, the value printed on the ordi- 
nate should be multiplied Dy 10 when the intercepts of the linear instan- 
taneous efficiency curves are being evaluated (these values range from 
to 100 percent). 

The collector array operating points, X, are calculated eacn scan by the 

equation 

X - (T f>1 - T a ) / I (4) 

where: 

T- i is the inlet temperature cf the collector array transport 
fluid (°F) 



T is tne temperature of the ambient air (°F) 
a 

I is the insolation rate (Btu/ft 2 -hr). 



25 





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Examination of the operating point histogram indicates that the predominant 
region of collector array operation occurred for operating points between 
0.10 to 0.20 (64 percent of the time). This leads to the expectation that 
the operational collector array efficiency would typically be on the order 
of 0.30, which is approximately 11 percent above the value of 0.27 presented 
in Table 5.3.1-1. 

The long-term first order curve shown in Figure 5.3.1-1 has a slightly less 
negative slope than the curve derived from single panel laboratory test data. 
This is attributable to lower losses resulting from array effects. The lab- 
oratory predicted instantaneous efficiency is not in close agreement with the 
curves derived from actual field operation. This indicates that the labora- 
tory derived curves might not be useful for design purposes in an array con- 
figuration of this type. 

It is suspected that the irregular operation of pump PI may have contributed 
to the relatively poor collector performance noted in this analysis. 

Additional information concerning collector array analysis in general may be 
found in a forthcoming paper [13] that describes collector array analysis pro- 
cedures in detail and presents the results of analysis performed on numerous 
collector array installations across the United States. 



27 



5.3.2 Storage Subsystem 

Storage subsystem performance is described by comparison of energy to 
storage, energy from storage and change in stored energy. The ratio of 
the sum of energy from storage and change in stored energy to energy to 
storage is defined as storage efficiency, n c - This relationship is ex- 
pressed in the equation 

n s ■ (AQ ♦ Q so )/Q si (5) 

where: 

AQ = change in stored energy. This is the difference in 
the estimated stored energy during the specified 
reporting period, as indicated by the relative 
temperature of the storage medium (either positive 
or negative value) (STECH) 

Q 6 = energy from storage. This is the amount of energy 
extracted by the load subsystem from the primary 
storage medium (STEO) 

Q j = energy to storage. This is the amount of energy 

(both solar and auxiliary) delivered to the primary 
storage medium (STEI). 

Evaluation of the system storage performance under actual transient 
system operation and weather conditions can be performed using the 
parameters listed above. The utility of these measured data in eval- 
uation of the overall storage design can be illustrated in the deriva- 
tion presented below. 

The overall thermal properties of the storage subsystem design can be 
derived empirically as a function of storage average temperature (average 
storage temperature for the reporting period) and the ambient temperature 
1n the vicinity of the storage tank. 



28 



An effective storage heat transfer coefficient (C) for the storage sub- 
system can be defined as follows: 

C - (Q si -q so -AQ s )/[(T s - T.) x t] £V (6) 

where : 

C = effective storage heat transfer coefficient 

Q j •=■ energy to storage (STEI) 

Q = energy from storage (STEO) 

AQ = change in stored energy (STECH) . 

T = storage average temperature (TS) 

T_ = average ambient temperature in the 
a 

vicinity of storage (TE) 

t = number of hours in the month (HM). 

The effective storage heat transfer coefficient is comparable to the heat 
loss rate defined in ASHRAE Standard 94-77 [6]. It has been calculated 
for each month in the report period and included, along with Stroage Average 
Temperature, in Table 5.3.2-1. 

The Blakedale Professional Center thermal storage consists of a 5,000 gallon 
tank that is buried adjacent to the parking lot. The tank is insulated with 
four inches of polyurethane foam and a waterproof coating. 



29 



2 





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Heat Loss 

Coefficient 

(Btu/Hr-°F) 


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Temperature 

(°F) 


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30 



As discussed in Section 2, the energy collection and storage subsystem was 
operational from October 16, 1978 through March 24, 1979 and after 
March 30, 1979, although pump PI did not always start automatically after 
mid December. The storage efficiency ranged from 0.10 for February to 
0.57 for March and averaged 0.46 for this six-month period. 

In general, the energy to storage was less than would be expected due to 
the unintentional rejection of stored energy resulting from improper op- 
eration of pump PI over the six-month period. Similarly, the energy 
extracted from storage was less than expected due to the inconsistent 
manual operation of pump P2 during February. Prior to mid January, the 
energy extracted from storage was greater than expected due to a space 
heating control system mode which removed energy from storage whenever 
there was a demand for space heating. The same situation existed in March, 
but was due to excessive manual operation of pump P2. The original control 
system design permitted the removal of solar energy from thermal storage 
whenever there was a demand for heating regardless of the temperature of 
the stored water. These factors had a corresponding impact on the effective 
storage heat loss coefficient. 



31 



5.3.3 Hot Water Subsystem 

The performance of the hot water subsystem is described by comparing the 
amount of solar energy supplied to the subsystem with the energy required 
to satisfy the total hot water load. The energy required to satisfy the 
total load consists of both solar energy and auxiliary thermal energy. 
The ratio of solar energy supplied to the load to the total load is defined 
as the hot water solar fraction. The calculated hot water solar fraction 
is the indicator of performance for the subsystem because it defines the 
percentage of the total hot water load supported by solar energy. 

The Blakedale Professional Center domestic hot water heating subsystem con- 
sists of a heat exchanger in the space heating subsystem thermal storage 
and a 40-gallon conventional electric water heater. The domestic hot water 
preheating mode (Mode 4) is entered when there is a requirement for hot 
water. This mode is terminated when the requirement for hot water is satis- 
fied. 

Except. for one week, the domestic hot water heating subsystem was operational 
over the entire six-month period. However, there was essentially no require- 
ment for hot water, as evidenced by the fact that the resident contractor did 
not operate the electric water heater. An insignificant amount of solar 
energy was removed from thermal storage whenever the hot water faucets were 
opened. This load is neglected, and assumed to be zero. As a result, the 
associated performance factors are zero. 



32 



5.3.4 Space Heating Subsystem 

The performance of the space heating subsystem is described by comparing 
the amount of solar energy supplied to the subsystem with the energy re- 
quired to satisfy the total space heating load. The energy required to 
satisfy the total load consists of both solar energy and auxiliary thermal 
energy. The ratio of solar energy supplied to the load to the total load 
is defined as the heating solar fraction. The calculated heating solar 
fraction is the indicator of performance for the subsystem because it de- 
fines the percentage of the total space heating load supported by solar 
energy. The performance of the space heating subsystem is presented in 
Table 5.3.4-1. 

The Blakedale Professional Center space heating subsystem consists of a 
solar supplied heat exchanger in an existing air-handling unit, a 10-ton 
heat pump and a 36-kilowatt electric resistance heater. Solar energy is 
supplied when Storage-to-Office area mode (Mode 2) is entered. This mode 
is terminated when the supply air temperature is greater than 120°F, or 
the requirement for heat is satisfied. There is no direct collector to 
load solar energy mode. 

The space heating subsystem was operational from October 18, 1978 through 
December 26, 1978; from January 2, 1979 through March 24, 1979; and after 
March 30, 1979. The resident contractor did not consistently monitor the 
requirement for space heating and implement manual control of the solar 
energy in storage from mid January through February. The solar fraction of 
the load ranged from a low of three percent in February to a maximum of 72 
percent in November and averaged 14 percent. During the six-month reporting 
period, solar energy provided 12.39 million Btu of the 86.54 million Btu 
space heating subsystem load. 

In general, the solar energy used was less than nominal due to the inconsis- 
tent manual operation of pump P2 during February. However, the solar energy 
used was larger than nominal (due to the original space heating control 
system design) prior to mid January and larger than nominal in March due to 



33 



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34 



the manual operation of pump P2. The original control system permitted the 
removal of solar energy from thermal storage whenever there was a demand 
for heating regardless of the temperature of the water in storage. 



35 



5.4 Operating Energy 

Operating energy for the Blakedale Professional Center solar energy 
system is defined as the energy required to transport solar energy to 
the point of use. Total operating energy for this system consists of 
energy collection and storage subsystem operating energy and space 
heating subsystem operating energy. Operating energy is electrical 
energy that is used to support the subsystems without affecting their 
thermal state. Measured monthly values for subsystem operating energy 
are presented in Table 5.4-1. 

At the Blakedale Professional Center, the energy collection and storage 
subsystem consumed 1.40 million Btu of electrical energy to operate 
Pump PI. This operating energy was larger than nominal due to the 
anomalous operation of pump PI over this six-month period. 

The domestic hot water heating subsystem does not require any operating 
energy and, hence, did not consume any electrical energy. 

The space heating subsystem consumed 6.86 million Btu of electrical energy 
to operate pump P2 and blowe** Bl in the air-handling unit. In general, 
this operating energy was larger than expected due to the excessive 
operation of pump P2 after February, although the operation of this 
pump was intermittent during February. 

A total of 8.26 million Btu of electrical operating energy was required 
to support operation of the complete system during the reporting period. 



36 





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Total System 
Operating Energy 
. (Million Btu) 


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37 



5.5 Energy Savings 

Solar energy system savings are realized whenever energy provided by the 
solar energy system is used to meet system demands which would otherwise 
be met by auxiliary energy sources. The operating energy required to pro- 
vide solar energy to the load subsystems is subtracted from the solar en- 
ergy contribution, and the resulting energy savings are adjusted to reflect 
the coefficient of performance (COP) of the auxiliary source being supplanted 
by solar energy. 

At the Blakedale Professional Center, the space heating subsystem contains a 
heat pump and an electric resistance heater to provide auxiliary thermal en- 
ergy. The COP for the heat pump was considered to be equal to two for Octo- 
ber, November, December and January. For February and March, this COP was 
calculated as a function of the ambient (outside) temperature. The resis- 
tance heater was considered to be 100 percent efficient for computational 
purposes. 

Electrical energy savings for the six-month reporting period are presented 
in Table 5.5-1. The space heating subsystem saved a total of 6.10 million 
Btu of electrical energy which resulted in a net savings of 4.69 million 
Btu (1,375 kwh) after the operating energy for the energy collection and 
storage subsystem is deducted. This is equivalent to 15.62 million Btu of 
fossil energy at the source of power generation. In general, the electrical 
energy savings were somewhat low due to the reasons discussed in the previ- 
ous section. 



38 





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39 



6. REFERENCES 

1. U.S. Department of Energy, National Solar Data Network , Prepared 
under Contract Number EG-77-C-01-4049, by IBM Corporation, 
December, 1977. 

2. J. T. Smok, V. S. Sohoni, J. M. Nash, "Processing of Instrumented 
Data for the National Solar Heating and Cooling Demonstration 
Program," Conference on Performance Monitoring Techniques for 
Evaluation of Solar Heating and Cooling Systems, Washington, D.C., 
April, 1978. 

3. E. Streed, et. al . , Thermal Data Requirements and Performance 
E valuation Procedures for the National Solar Heating and Cooling 
Demonstration Program , NBSIR 76-1137, National Bureau of Standards, 
Washington, August, 1976. 

4^ Mears, J. C. Reference Monthly Environmental Data for Systems in 
the National Solar Data Network . Department of Energy report 
SOLAR/0019-79/36. Washington, D.C., 1979. 

5. ASHRAE Standard 93-77 , Methods of Testing to Determine the Thermal 
Performance of Solar Collectors , The American Society of Heating, 
Refrigeration and Air Conditioning Engineers, Inc., New York, NY, 
1977. 

6. ASHRAE Standard 94-77 , Methods of Testing Thermal Storage Devices 
Based on Thermal Performance , The American Society of Heating, 
Refrigeration and Air Conditioning Engineers, Inc., New York, NY, 
1977. 

7.* Monthly Performance Report , Blakedale Professional Center , 

SOLAR/2014-78/10, Department of Energy, Washington (October 1978). 



41 



8.* Monthly Performance Report , Blakedale Professional Center , 

SOLAR/201 4-78/1 1, Department of Energy, Washington (November 1978). 

9.* Monthly Performance Report , Blakedale Professional Center , 

SOLAR/2014-78/12, Department of Energy, Washington (December 1978). 

10.* Monthly Performance Report , Blakedale Professional Center , 

SOLAR/2014-79/01 , Department of Energy, Washington (January 1979). 

11.* Monthly Performance Report , Blakedale Professional Center , 

SOLAR/201 4-79/02, Department of Energy, Washington (February 1979). 

12.* Monthly Performance Report , Blakedale Professional Center , 

SOLAR/2014-79/03, Department of Energy, Washington (March 1979). 

13. McCumber, W. H. Jr., "Collector Array Performance for Instrumented 
sites of the National Solar Heating and Cooling Demonstration 
Program," to be published and distributed at the 1979 Solar Update 
Conference. 



* Copies of these reports may be obtained from Technical Information Center, 
P. 0. Box 62, Oak Ridge, Tennessee 37830. 



42 



APPENDIX A 

DEFINITION OF PERFORMANCE FACTORS AND SOLAR TERMS 

COLLECTOR ARRAY PERFORMANCE 

The collector array performance is characterized by the amount of solar energy 
collected with respect to the energy available to be collected. 

t INCIDENT SOLAR ENERGY (SEA) is the total insolation available on the 
gross collector array area. This is the area of the collector 
array energy-receiving aperture, including the framework which is 
an integral part of the collector structure. 

t OPERATIONAL INCIDENT ENERGY (SEOP) is the amount of solar energy 
incident on the collector array during the time that the col- 
lector loop is active (attempting to collect energy). 

• COLLECTED SOLAR ENERGY (SECA) is the thermal energy removed from 
the collector array by the energy transport medium. 

• COLLECTOR ARRAY EFFICIENCY (CAREF) is the ratio of the energy col- 
lected to the total solar energy incident on the collector array. 
It should be emphasized that this efficiency factor is for the 
collector array, and available energy includes the energy incident 
on the array when the collector loop is inactive. This efficiency 
must not be confused with the more common collector efficiency 
figures which are determined from instantaneous test data obtained 
during steady state operation of a single collector unit. These 
efficiency figures are often provided by collector manufacturers 
or presented in technical journals to characterize the functional 
capability of a particular collector design. In general, the 
collector panel maximum efficiency factor will be significantly 
higher than the collector array efficiency reported here. 



A-l 



STORAGE PERFORMANCE 

The storage performance is characterized by the relationships among the energy 
delivered to storage, removed from storage, and the subsequent change in the 
amount of stored energy. 

t ENERGY TO S TORAGE (STEi) is the amount of energy, both solar and 
auxiliary, delivered to the primary storage medium. 

• EN ERGY FROM STORAGE (STEO) is the amount of energy extracted by 
the load subsystems from the primary storage medium. 

§ CHANGE IN STORED ENERGY (STECH) is the difference in the estimated 
stored energy during the specified reporting period, as indicated 
by the relative temperature of the storage medium (either positive 
or negative value). 

• STORAGE AVERAGE TEMPERATU RE (TST) is the mass-weighted average 
temperature of the primary storage medium. 

• STOR AGE EFFICIENCY (STEFF) is the ratio of the sum of the energy 
removed from storage and the change in stored energy to the 
energy delivered to storage. 



A-2 



ENERGY COLLECTION AND STORAGE SUBSYSTEM 

The energy collection and storage subsystem (ECSS) is composed of the col- 
lector array, the primary storage medium, the transport loops between these, 
and other components in the system design which are necessary to mechanize 
the collector and storage equipment. 

• INCIDENT SOLAR ENERGY (SEA) is the total solar energy incident on 
the gross collector array area. This is the area of the collector 
array energy- removing aperature, including the framework, which is 
an integral part of the collector structure. 

t AMBIENT TEMPERATURE (TA) is the average temperature of the outdoor 
environment at the site. 

• ENERGY TO LOADS (SEL) is the total thermal energy transported 
from the ECSS to all load subsystems. 

• AUXILIARY THERMAL ENERGY TO ECSS (CSAUX) is the total auxiliary 
supplied to the ECSS, including auxiliary energy added to the 
storage tank, heating devices on the collectors for freeze- 
protection, etc. 

• ECSS OPERATING ENERGY (CSOPE) is the critical operating energy 
required to support the ECSS heat transfer loops. 



A-3 



HOT WATER SUBSYSTEM 

The hot water subsystem 1s characterized by a complete accounting of the 
energy flow to and from the subsystem, as well as an accounting of internal 
energy. The energy Into the subsystem 1s composed of auxiliary fossil fuel 
and electrical auxiliary thermal energy, and the operating energy for the 
subsystem. In addition, the solar energy supplied to the subsystem, along 
with solar fraction, is tabulated. The load of the subsystem is tabulated 
and used to compute the estimated electrical and fossil fuel savings of the 
subsystem. The load of the subsystem is further Identified by tabulating 
the supply water temperature, the outlet hot water temperature, and the total 
hot water consumption. 

t HOT WATER LOAD (HWL) 1s the amount of energy required to heat the 
amount of hot water demanded at the site from the incoming tempera- 
ture to the desired outlet temperature. 

• SOLAR FRACTION OF LOAD (HWSFR) 1s the percentage of the load demand 
which is supported by solar energy. 

t SOLAR ENERGY USED (HWSE) 1s the amount of solar energy supplied to 
the hot water subsystem. 

t OPERATING ENERGY (HWOPE) 1s the amount of electrical energy required 
to support the subsystem, (e.g., fans, pumps, etc.) and which is 
not Intended to affect directly the thermal state of the subsystem. 

• AUXILIARY THERMAL USED (HWAT) 1s the amount of energy supplied to 
the major components of the subsystem in the form of thermal energy 
1n a heat transfer fluid, or Its equivalent. This term also in- 
cludes the converted electrical and fossil fuel energy supplied to 
the subsystem. 

§ AUXILIARY ELECTRICAL FUEL (HWAE) 1s the amount of electrical energy 
supplied directly to the subsystem. 



A-4 



t ELECTRICAL ENERGY SAVINGS (HWSVE) is the estimated difference 

between the electrical energy requirements of an alternative con- 
ventional system (carrying the full load) and the actual electri- 
cal energy required by the subsystem. 

• SUPPLY WATER TEMPERATURE (TSW) is the average inlet temperature 
of the water supplied to the subsystem. 

• AVERAGE HOT WATER TEMPERATURE (THW) is the average temperature of 
the outlet water as it is supplied from the subsystem to the load. 

• HOT WATER USED (HWCSM) is the volume of water used. 



A-5 



SPACE HEATING SUBSYSTEM 

The space heating subsystem is characterized by performance factors accounting 
for the complete energy flow to and from the subsystem. The average building 
temperature and the average ambient temperature are tabulated to indicate the 
relative performance of the subsystem in satisfying the space heating load and 
in controlling the temperature of the conditioned space. 

§ SPACE HEATING LOAD (HL) is the sensible energy added to the air in 
the building. 

• SOLAR FRACTION OF LOAD (HSFR) is the fraction of the sensible energy 
added to the air in the building derived from the solar energy system. 

t SOLAR ENERGY USED (HSE) is the amount of solar energy supplied to 
the space heating subsystem. 

t OPERATING ENERGY (HOPE) is the amount of electrical energy required 
to support the subsystem, (e.g., fans pumps, etc.) and which is not 
intended to affect directly the thermal state of the subsystem. 

• AUXILIARY THERMAL USED (HAT) is the amount of energy supplied to 
the major components of the subsystem in the form of thermal energy 
in a heat transfer fluid or its equivalent. This term also includes 
the converted electrical and fossil fuel energy supplied to the 
subsystem. 

• AUXILIARY ELECTRICAL FUEL (HAE) is the amount of electrical energy 
supplied directly to the subsystem. 

t ELECTRICAL ENERGY SAVINGS (HSVE) is the estimated difference between 
the electrical energy requirements of an alternative conventional 
system (carrying the full load) and the actual electrical energy 
required by the subsystem. 



A-6 



• . BUILDING TEMPERATURE (TB) is the average heated space dry bulb 

temperature. 

• AMBIENT TEMPERATURE (TA) is the average ambient dry bulb tempera- 
ture at the site. 



A-7 



ENVIRONMENTAL SUMMARY 

The environmental summary is a collection of the weather data which is 
generally instrumented at each site in the program. It is tabulated in 
this data report for two purposes--as a measure of the conditions prevalent 
during the operation of the system at the site, and as an historical 
record of weather data for the vicinity of the site. 

c TOTAL INSOLATION (SE) is accumulated total solar energy inci- 
dent upon the gross collector array measured at the site. 

c AMBIENT TEMPERATURE (TA) is the average temperature of the 
environment at the site. 

• WIND DIRECTION (WDIR) is the average direction of the prevail- 
ing wind. 

• WIND SPEED (WIND) is the average wind speed measured at the .site. 

• DAYTIME AMBIENT TEMPERATURE (TDA) is the temperature during the 
period from three hours before solar noon to three hours after 
solar noon. 



A-8 



APPENDIX B 

SOLAR ENERGY SYSTEM PERFORMANCE EQUATIONS FOR THE 
BLAKEDALE PROFESSIONAL CENTER 



I. INTRODUCTION 

Solar energy system performance is evaluated by performing energy balance 
calculations on the system and its major subsystems. These calculations 
are based on physical measurement data taken from each subsystem every 320 
seconds. This data is then numerically combined to determine the hourly, 
daily, and monthly performance of the system. This appendix describes the 
general computational methods and the specific energy balance equations 
used for this evaluation. 

Data samples from the system measurements are numerically integrated to 
provide discrete approximations of the continuous functions which charac- 
terize the system's dynamic behavior. This numerical integration is per- 
formed by summation of the product of the measured rate of the appropriate 
performance parameters and the sampling interval over the total time period 
of interest. 

There are several general forms of numerical integration equations which 
are applied to each site. These general forms are exemplified as follows: 
The total solar energy available to the collector array is given by 

SOLAR ENERGY AVAILABLE = (1/60) z [1001 x AREA] x At 

where 1001 is the solar radiation measurement provided by the pyranometer 

2 
in Btu/ft -hr, AREA is the area of the collector array in square feet, 

At is the sampling interval in minutes, and the factor (1/60) is included 

to correct the solar radiation "rate" to the proper units of time. 



B-l 



Similarly, the energy flow within a system is given typically by 

COLLECTED SOLAR ENERGY = Z [Ml 00 x AH] x Ax 

where Ml 00 is the mass flow rate of the heat transfer fluid 1n lb /min and 

m 

aH 1s the enthalpy change, 1n Btu/lb , of the fluid as 1t passes through 
the heat exchanging component. 

For a liquid system aH 1s generally given by 

AH = C AT 

where C_ 1s the average specific heat, in Btu/(lb -°F), of the heat 
transfer fluid and aT, 1n °F, is the temperature differential across 
the heat exchanging component. 

For an air system aH 1s generally given by 

iH ■ H a< T out> " H a< T 1n> 

where H (T) is the enthalpy, in Btu/lb , of the transport air 
evaluated at the inlet and outlet temperatures of the heat ex- 
changing component. 

H (T) can have various forms, depending on whether or not the humidity ratio 
a 

of the transport air remains constant as it passes through the heat exchan- 
ging component. 



B-2 



For electrical power, a general example 1s 

ECSS OPERATING ENERGY = (3413/60) i [EP100] x At 

where EP100 1s the power required by electrical equipment in kilowatts 
and the two factors (1/60) and 3413 correct the data to Btu/min. 

These equations are comparable to those specified in "Thermal Data Require- 
ments and Performance Evaluation Procedures for the National Solar Heating 
and Cooling Demonstration Program." This document, given in the list of 
references, was prepared by an inter-agency committee of the government, 
and presents guidelines for thermal performance evaluation. 

Performance factors are computed for each hour of the day. Each numerical 
integration process, therefore, is performed over a period of one hour. 
Since long-term performance data is desired, it is necessary to build these 
hourly performance factors to daily values. This is accomplished, for 
energy parameters, by summing the 24 hourly values. For temperatures, the 
hourly values are averaged. Certain special factors, such as efficiencies, 
require appropriate handling to properly weight each hourly sample for the 
daily value computation. Similar procedures are required to convert daily 
values to monthly values. 



B-3 



EQUATIONS USED IN MONTHLY PERFORMANCE REPORT 



NOTE: - MEASUREMENT NUMBERS REFERENCE SYSTEM SCHEMATIC FIGURE 3-1 

AVERAGE AMBIENT TEMPERATURE (°F) 

TA = (1/60) x I T001 x At 
AVERAGE BUILDING TEMPERATURE (°F) 

TB = (1/60) x E T600 x At 
DAYTIME AVERAGE AMBIENT TEMPERATURE (°F) 

TDA = (1/360) x Z T001 x At 

FOR + 3 HOURS FROM SOLAR NOON 
INCIDENT SOLAR ENERGY PER SQUARE FOOT (BTU/FT 2 ) 

SE = (1/60) x E 1001 x At 
OPERATIONAL INCIDENT SOLAR ENERGY (BTU) 

SEOP = (1/60) x I [1001 x CLAREA] x At 
WHEN THE COLLECTOR LOOP IS ACTIVE 
ENTHALPY FUNCTION FOR WATER (BTU/LBM) 



T 2 
HWD(T 2 , T^ * T / c C p (T)dT 



THIS FUNCTION COMPUTES THE ENTHALPY CHANGE OF WATER AS IT 
PASSES THROUGH A HEAT EXCHANGING DEVICE. 
SOLAR ENERGY COLLECTED BY THE ARRAY (BTU) 

SECA = Z [M100 x HWD (T150, T100)] x At 
ECSS OPERATING ENERGY (BTU) 

CSOPE = 56.8833 x I EP101 x At 



B-4 



SOLAR ENERGY TO STORAGE (BTD) 

STEI = z [MIOO x HWD(T101, T151)] x At 
SOLAR ENERGY FROM STORAGE 

ST£0 = z [M300 x HWD(T351, T350) + M400 x HWD(T400, T450)] x Ax 
AVERAGE TEMPERATURE OF STORAGE (°F) 

TST = (1/60) x Z [(T201 + T202 + T203)/3] x At 
SOLAR ENERGY TO HOT WATER SUBSYSTEM (BTU) 

HWSE = l [M300 x HWD(T351, T350)] x At 
HOT WATER LOAD (BTU) 

HWL = I [M300 x HWD(T310, T350)^ x At 
HOT WATER AUXILIARY ELECTRIC ENERGY (BTU) 

HWAE = 56.8833 x I EP300 x At 
HOT WATER CONSUMED (GALLONS) 

HWCSM = E [M300/RH0(T351)] x At 
SOLAR ENERGY TO SPACE HEATING SUBSYSTEM (BTU) 

HSE = Z [M401 x HWD(T451, T401)] x At 
SPACE HEATING AUXILIARY THERMAL ENERGY (BTU) 
HAT = 0.7 x 56.8833 x I EP403 x At 

WHEN HEAT PUMP IS OPERATING 
HAT = 56.8833 x Z EP403 x At 

WHEN HEAT STRIPS ARE OPERATING 
HUMIDITY RATIO FUNCTION (BTU/LBM-°F) 
HRF = 0.24 + 0.444 x HR 

WHERE 0.24 IS THE SPECIFIC HEAT AND HR IS THE HUMIDITY RATIO 
OF THE TRANSPORT AIR. THIS FUNCTION IS USED WHENEVER THE 
HUMIDITY RATIO WILL REMAIN CONSTANT AS THE TRANSPORT AIR FLOWS 
THROUGH A HEAT EXCHANGING DEVICE 



B-5 



SPACE HEATING LOAD (BTU) 

HL = Z [M600 x HRF x (T602 - T650)] x Ax 
SPACE HEATING SUBSYSTEM OPERATING ENERGY (BTU) 

HOPE = 56.8833 x I [EP401 + EP402] x At 
SPACE HEATING SUBSYSTEM AUXILIARY ELECTRICAL FUEL ENERGY (BTU) 

HAE = 56.8833 x I EP402 x At 
COLLECTED SOLAR ENERGY (BTU/FT 2 ) 

SEC = SECA/CLAREA 
INCIDENT SOLAR ENERGY ON COLLECTOR ARRAY (BTU) 

SEA = CLAREA x SE 
COLLECTOR ARRAY EFFICIENCY 

CAREF = SECA/SEA 
SUPPLY WATER TEMPERATURE (°F) 

TSW = T310 
HOT WATER TEMPERATURE (°F) 

THW = T350 

BOTH TSW AND THW ARE COMPUTED ONLY WHEN FLOW EXISTS IN THE 
SUBSYSTEM, OTHERWISE THEY ARE SET EQUAL TO THE VALUES OBTAINED 
DURING THE PREVIOUS FLOW PERIOD. 
CHANGE IN STORED ENERGY (BTU) 

STECH = STOCAP x (STOTP - STOTP ) 

WHERE THE SUBSCRIPT REFERS TO A PRIOR REFERENCE VALUE 
SOLAR ENERGY TO LOADS (BTU) 

SEL = HWSE + HSE 
ENERGY DELIVERED TO LOAD SUBSYSTEMS FROM ECSS (BTU) 

CSEO = HWSE + HSE 



B-6 



STORAGE EFFICIENCY 

STEFF = (STECH + STEO)/STEI 
ECSS SOLAR CONVERSION EFFICIENCY 

CSCEF = SEL/SEA 
HOT WATER AUXILIARY THERMAL ENERGY (BTU) 

HWAT = HWAE 
HOT WATER ELECTRICAL ENERGY SAVINGS (BTU) 

HWSVE = HWSE 
HOT WATER SOLAR FRACTION (PERCENT) 

HWSFR = 100 x HWTKSE/(HWTKSE + HWTKAUX) 

WHERE HWTKSE AND HWTKAUX REPRESENT THE CURRENT SOLAR AND 
AUXILIARY ENERGY CONTENT OF THE HOT WATER TANK 
SPACE HEATING SUBSYSTEM ELECTRICAL ENERGY SAVINGS (BTU) 

HSVE = HPFRAC x HL/HPCOP + (1-HPFRAC) x HL - (HAE + HOPE) 
SPACE HEATING SOLAR FRACTION (PERCENT) 

HSFR = 100 x (HSE/HL) 
AUXILIARY THERMAL ENERGY TO LOADS (BTU) 

AXT = HWAT + HAT 
AUXILIARY ELECTRICAL ENERGY TO LOADS (BTU) 

AXE = HAE + HWAE 
SYSTEM OPERATING ENERGY (BTU) 

SYSOPE = HOPE + CSOPE 
SYSTEM LOAD (BTU) 

SYSL = HL + HWL 
TOTAL ENERGY CONSUMED (BTU) 

TECSM = SYSOPE + AXE + SECA 



B-7 



TOTAL ELECTRICAL ENERGY SAVINGS (BTU) 
TSVE = HWSVE + HSVE - CSOPE 

SOLAR FRACTION OF SYSTEM LOAD (PERCENT) 
SFR = (HL x HSFR + HWL x HWSFR)/SYSL 

SYSTEM PERFORMANCE FACTOR 

SYSPF = SYSL/((AXE + SYSOPE) x 3.33) 



B-8 



APPENDIX C 
LONG-TERM AVERAGE WEATHER CONDITIONS 



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